-5x^2+120=-40

Solution for -5x^2+120=-40 equation:

-5x^2+120=-40

We move all terms to the left:

-5x^2+120-(-40)=0

We add all the numbers together, and all the variables

-5x^2+160=0

a = -5; b = 0; c = +160;
Δ = b2-4ac
Δ = 02-4·(-5)·160
Δ = 3200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-5}=\frac{0-40\sqrt{2}}{-10}
=-\frac{40\sqrt{2}}{-10}
=-\frac{4\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-5}=\frac{0+40\sqrt{2}}{-10}
=\frac{40\sqrt{2}}{-10}
=\frac{4\sqrt{2}}{-1}
$